An Introduction to Continuous-Time Stochastic Processes Theory, Models, and Applications to Finance, Biology, and Medicine
Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. From reviews of previous editions: "The book is ... an account of fundamental concepts as they appea...
Main Authors: | , |
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Format: | eBook |
Language: | English |
Published: |
New York, NY
Birkhäuser
2015, 2015
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Edition: | 3rd ed. 2015 |
Series: | Modeling and Simulation in Science, Engineering and Technology
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Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Summary: | Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. From reviews of previous editions: "The book is ... an account of fundamental concepts as they appear in relevant modern applications and literature. ... The book addresses three main groups: first, mathematicians working in a different field; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications." —Zentralblatt MATH. This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics, and epidemics * Agent-based models New to the Third Edition: * Infinitely divisible distributions * Random measures * Levy processes * Fractional Brownian motion * Ergodic theory * Karhunen-Loeve expansion * Additional applications * Additional exercises * Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Edition will be of interest to a broad audience of students, pure and applied mathematicians, and researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduate courses, as well as European Masters courses (according to the two-year-long second cycle of the “Bologna Scheme”), the work may also be used for self-study or as a reference. |
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Physical Description: | XVI, 482 p. 14 illus online resource |
ISBN: | 9781493927579 |